Weak Convergence of Set-Valued Functions and Control

Weak convergence on the space of integrably bounded set-valued functions is defined. Generalizations of results of weak convergence of real-valued integrable functions are obtained in the set-valued case. The results are applied to the characterization of the continuous dependence of the attainable...

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Bibliographic Details
Main Author: Artstein,Zvi
Format: Report
Language:English
Subjects:
Control theory
Convergence
Functions(Mathematics)
Graph theory
Linear systems
Measure theory
Set theory
Theorems
Theoretical Mathematics
Weak convergence
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Summary:Weak convergence on the space of integrably bounded set-valued functions is defined. Generalizations of results of weak convergence of real-valued integrable functions are obtained in the set-valued case. The results are applied to the characterization of the continuous dependence of the attainable set of a linear control system on the restraint set. It is shown that the weak convergence of the restraint set is a sufficient condition for the uniform convergence of the attainable set, and under the additional condition of uniform integrability the weak convergence is also a necessary condition. (Author)